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Here we will learn about place value, including how to use it for integers, decimals and measures.

There are also place value worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Place value **is the value of each digit within a number.

A number is made up of digits, for example the two-digit number 54 (fifty four), has two digits, 5 and 4. We need to be able to say the value of each digit within the number as this can help with understanding how large or small the number is and can help us to order numbers.

To determine the value of a digit within a number we use a place value chart.

For example, the number 54 would look like this, where the 4 is in the ones column, and the 5 is in the tens column.

This means that the number 54 is equivalent to 5 tens and 4 ones.

5 tens is the same as 5\times{10}=50 and 4 ones is the same as 4\times{1}=4.

Adding the two values of 50 and 4 gives us the number 54.

To write the place value of a digit within a number, we must know the column that the digit is sitting in. We determine this by lining up the ones column first, and then we write every other digit in the correct column next to it.

Here we will consider the place value of digits to the **left of the decimal point.**

**Using a comma or a space**

The comma or space is used to help the reader to read a number efficiently. They are used for the digits to the left of the decimal point, separating 3 digits at a time.

For example,

The number 9456382 is easier to read by placing a space after the millions digit (9), and a space after the thousands digit (6). This would give us the number 9 \ 456 \ 382 which would read as,

nine million, four hundred and fifty six thousand, three hundred and eighty two.

**Zero place holder**

If the first digit of a number is to the **left of the decimal point **(ones, ten thousands, millions etc), we do not need to write a zero before the start of the number.

This is because, for example. the number 293 is exactly the same as the number 000293 and so the zeros before the digit 2 in the hundreds column are unnecessary.

However, if the value within the column is 0, we must write a zero within that place value.

For example, 5084 is the number five thousand and eighty four.

If we missed the 0 out of the number, we would get the number 584, read as five hundred and eighty four, which is a different number.

**Larger numbers**

We can use place value to represent very large numbers.

Here we are considering the place value of digits to the** right of the decimal point**.

**Reading decimals**

Decimals are read digit by digit.

For example, the decimal number 12.34 would be read as twelve point three four, and **not **twelve point thirty four. This is the reason why we do not separate the decimals using a comma or a space.

For small numbers that contain a lot of zeros such as 0.003, we would pronounce this number as zero point zero zero three.

**Zero place holder**

For decimals, we must write a 0 placeholder in any column between the decimal point and the first non-zero digit to the right of the decimal point. If there are no ones, we must also write a zero in the ones column.

For example, the number four thousandths is written as 0.004 which has a 0 place holder in the ones, tenths and hundredths columns.

**Very small numbers**

We can use place value to represent very small numbers.

In order to write the value of a digit in a number:

**Locate the digit within the number.****Recall the place value of that column.****Write the value of the digit.**

Get your free place value worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free place value worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEWrite down the value of the digit 3 in the four-digit number 4163.

**Locate the digit within the number.**

2**Recall the place value of that column.**

The 3 is in the ones column.

3**Write the value of the digit.**

The value of the digit 3 in the number 4163 is 3 ones, or 3.

Write down the value of the digit 4 in the number 385,431.

**Locate the digit within the number.**

**Recall the place value of that column.**

The 4 is in the hundreds column.

**Write the value of the digit.**

The value of the digit 4 in the number 385431 is four hundred, or 400.

Write down the value of the digit 2 in the number 1,025,634.

**Locate the digit within the number.**

**Recall the place value of that column.**

The 2 is in the ten thousands column.

**Write the value of the digit.**

The value of the digit 2 in the number 1,025,634 is twenty thousand, or 20,000.

Write down the value of the digit 2 in the number 3.264.

**Locate the digit within the number.**

**Recall the place value of that column.**

The 2 is in the tenths column.

**Write the value of the digit.**

The value of the digit 2 in the number 3.264 is two tenths, or 0.2.

Write down the value of the digit 7 in the number 0.0783.

**Locate the digit within the number.**

**Recall the place value of that column.**

The 7 is in the hundredths column.

**Write the value of the digit.**

The value of the digit 7 in the number 0.0783 is seven hundredths, or 0.07.

Write down the value of the digit 4 in the number 10.05401.

**Locate the digit within the number.**

**Recall the place value of that column.**

The 4 is in the thousandths column.

**Write the value of the digit.**

The value of the digit 4 in the number 10.05401 is four thousandths, or 0.004.

**Thousands or thousandths**

Numbers to the right of the decimal point are parts of a whole and so they each end in ths. Numbers to the left of the decimal point do not end in ths as they are whole numbers.

**Including the digits after the required digit**

All of the digits after the required place value are sometimes wrongly included, for example the value of 4 in the number 243 is given as forty three, or 43.

The correct solution is forty, or 40.

**Including a ones column**

The first column to the right of the decimal point is the tenths column – there is no ones column.

For example, the value of the digit 2 in the number 3.524 may be given as two tenths or 0.02 which is incorrect. The correct answer is two hundredths, or 0.02.

**Place value** is part of our series of lessons to support revision on **rounding numbers**, and upper and lower bounds. You may find it helpful to start with the main rounding numbers lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Write the value of 2 in the number 475,321.

21

20

2

Two hundreds

The digit 2 is in the tens column.

2. Write the value of 1 in the number 1,000,253.

1,000

100000

1,000,000

One hundred thousand

The digit 1 is in the millions column.

3. Write the value of 3 in the number 483,201.

3,000

300

10,000

Ten thousand

The digit 3 is in the thousands column.

4. Write the value of 7 in the number 6.072.

Seven hundredths

Seven hundreds

Seven tenths

Seven tens

The digit 7 is in the hundredths column.

5. Write the value of 8 in the number 0.0008.

Eight thousandths

Eighty hundred

Eight ten thousandths

Eight tenths

The digit 8 is in the ten thousandths column.

6. Write the value of 4 in the number 4.825.

4

4000

Four thousandths

0.4

The digit 4 is in the ones column.

1. (a) Write in figures the number fifty seven thousand and four.

(b) Write in words the number 0.052.

(c) Write the value of the digit 4 in the number 5,846,732.

**(3 marks)**

Show answer

(a) 57,004

**(1)**

(b) Zero point zero five two

**(1)**

(c) 40,000 **or** forty thousand

**(1)**

2. (a) Calculate 0.43 \div 100.

(b) State the value of the digit from your answer to part (a) that is in the thousandths column.

**(2 marks)**

Show answer

(a) 0.0043

**(1)**

(b) 4 thousandths or 0.004

**(1)**

3. (a) Dom says

“The value of the digit 3 in the number 0.7534 is 3000 ”.

Is Dom correct?

Explain your answer.

(b) The record for a bobsleigh run on a track is 16.543 seconds. The record is beaten by 2 thousandths of a second.

What is the new record for the track?

**(5 marks)**

Show answer

(a)

No

**(1)**

Dom has stated that the 3 is in the thousands column whereas it is in the thousandths column (part of an integer) or 0.003 .

**(1)**

(b)

0.002

**(1)**

**(1)**

**(1)**

You have now learned how to:

- Understand and use place value for decimals, measures and integers of any size

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